In this work we compute several kinematic moments of inclusive
\(B \rightarrow X_c \ell \bar{\nu }_\ell \)  decays up to \(O(\alpha _s^3)\) . In particular we
consider for the first time higher order QCD corrections to \(q^2\)  moments. We
use the optical theorem to obtain analytic expressions for the moments as an
expansion in the parameter \(\delta =1-m_c/m_b\) . For most of the considered
observables, the series expansion in \(\delta \)  is sufficient to obtain precise
results for the coefficients of the perturbative expansion. However, for some
of the centralized moments, there are significant cancellations and our finite
expansion depth in \(\delta \)  does not allow for a determination of the
\(\alpha _s^3\)  corrections in a reliable way.
Note that also a calculation based on numerical methods might have
similar problems since also there in a first step the elementary moments are
computed with a finite numerical accuracy [1]}.
